1. Field of the Invention
This disclosure relates to computer technology for implementing computational fluid dynamics analysis.
2. Description of the Related Art
Computational fluid dynamics (CFD) analysis is a complex technology involving strongly coupled non-linear partial differential equations which perform computations in a finite difference form supported by a discrete grid domain containing complex geometric shapes.
CFD analysis is often applied to flows typical of aerospace systems. Such flows often are characterized by the Mach number, which may range from 0 to 25. Such flows often have high Reynolds numbers resulting in regions of laminar flow becoming turbulent flow. Boundary layers are created by flows along body and inlet surfaces. Internal flows may have adverse pressure gradients. Shock waves, accompanied by separation of the boundary layer, may be present at transonic, supersonic and hypersonic speeds. Real gas effects may become important at hypersonic Mach numbers. The geometry of the system may be complex and unsteady flow may be present.
The efficacy of the CFD analysis depends on the manner of subdivision of the three-dimensional space. The numerical approximation of the Navier-Stokes equation contains errors that depend on the local density of tetrahedral subdivision and the local flow situation. Often times, deficiency of density distribution in the space is known only after the completion of a CFD analysis. Practitioners of the art have long desired to have an accurate, fast, and robust tool to modify the grid by h-refinement or some other means. However, modern computational mesh may contain more than 100 million cells. It is a monumental task for practitioners of the art to analyze both the solution and the mesh to decide where and how to perform mesh refinement efficiently within a reasonable amount of time and with a reasonable amount of effort.
Another impediment to applying the h-refinement procedure for advanced CFD analysis is that the conventional method of refinement subdivides each targeted cell into eight parts. Should refinement be required again at the location of the original cell, two steps of division would result in 64 parts, an unwieldy number. To make matters worse, the rules for grid integrity would require the subdivision of neighboring cells into eight, four, or two parts at each step of h-refinement.
The foregoing examples of the related art and limitations related therewith are intended to be illustrative and not exclusive. Other limitations of the related art will become apparent to those of skill in the art upon a reading of the specification and a study of the drawings.
Embodiments of the present disclosure meet the long-felt need for an accurate, fast, and robust tool to modify the grid by h-refinement.